859,424 research outputs found
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Connection between complete and Moebius forms of gauge invariant operators
We study the connection between complete representations of gauge invariant
operators and their Moebius representations acting in a limited space of
functions. The possibility to restore the complete representations from Moebius
forms in the coordinate space is proven and a method of restoration is worked
out. The operators for transition from the standard BFKL kernel to the
quasi-conformal one are found both in Moebius and total representations.Comment: Changed title and a short paragraph in the section "Conclusion";
unchanged results. Version to appear on Nucl. Phys.
Many-spinon states and the secret significance of Young tableaux
We establish a one-to-one correspondence between the Young tableaux
classifying the total spin representations of N spins and the exact eigenstates
of the the Haldane-Shastry model for a chain with N sites classified by the
total spins and the fractionally spaced single-particle momenta of the spinons.Comment: 4 pages, 3 figure
Spectral Representations of One-Homogeneous Functionals
This paper discusses a generalization of spectral representations related to
convex one-homogeneous regularization functionals, e.g. total variation or
-norms. Those functionals serve as a substitute for a Hilbert space
structure (and the related norm) in classical linear spectral transforms, e.g.
Fourier and wavelet analysis. We discuss three meaningful definitions of
spectral representations by scale space and variational methods and prove that
(nonlinear) eigenfunctions of the regularization functionals are indeed atoms
in the spectral representation. Moreover, we verify further useful properties
related to orthogonality of the decomposition and the Parseval identity.
The spectral transform is motivated by total variation and further developed
to higher order variants. Moreover, we show that the approach can recover
Fourier analysis as a special case using an appropriate -type
functional and discuss a coupled sparsity example
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